Timeline for When is a topological space the homotopy colimit of an open covering?
Current License: CC BY-SA 4.0
10 events
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| Jun 19 at 11:18 | comment | added | Dylan Wilson | Since for some reason this post got bumped, just wanted to say that I was surprised to find what I have always thought of as "Lurie's Seifert-van Kampen theorem" as Proposition A.5 in Segal's paper on classifying spaces of foliations, from 1978. | |
| Jun 19 at 7:58 | comment | added | Martin Sleziak | The link to Lurie's Higher algebra seems to be dead - perhaps this would be a reasonable replacement: math.ias.edu/~lurie/papers/HA.pdf? I have added Wayback Machine link for the other dead link - but maybe it could be simply replaced by a link to arXiv:math/0111287. | |
| Jun 19 at 7:57 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
added a Wayback Machine link for the dead link
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| Nov 24, 2014 at 15:17 | comment | added | Ronnie Brown | The invariants I have dealt with are of: spaces with many base points; filtered spaces; and $n$-cubes of spaces. The first two are dealt with in the EMS Tract vol 15 (2011) on "Nonabelian algebraic topology:...", and were published first in 1967 and 1981, respectively. | |
| Nov 24, 2014 at 15:03 | comment | added | Ronnie Brown | My attitude to Seifer-van Kampen thoerems is that they are about direct computation of a strict homotopical invariant as an exact colimit. | |
| Nov 23, 2014 at 23:03 | comment | added | Marc Hoyois | I think it would be unfair not to call Lurie's theorem itself a higher Seifert-van Kampen theorem. Note that the result I've quoted is only a special case of half of the theorem. The other half (in the same special case) says that the actual colimit of the diagram of simplicial sets $Sing(C_U)$ is weakly equivalent to $Sing(X)$. | |
| Nov 23, 2014 at 22:36 | vote | accept | David Carchedi | ||
| Nov 23, 2014 at 20:42 | comment | added | Ronnie Brown | My question mathoverflow.net/questions/102295/… is relevant to your comment. Note that this sometimes called "small simplex" theorem has other proofs in the literature, and has not led to proofs of higher Seifert-van Kampen Theorems, to my knowledge. | |
| Nov 23, 2014 at 17:37 | history | edited | Marc Hoyois | CC BY-SA 3.0 |
added 252 characters in body
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| Nov 23, 2014 at 17:31 | history | answered | Marc Hoyois | CC BY-SA 3.0 |